Brauer–Manin obstruction for Wehler K3 surfaces of Markoff type

Abstract

Following a recent work of Fuchs, Litman, Silverman, and Tran, we study the Brauer–Manin obstruction for integral points on Wehler K3 surfaces of Markoff type. In particular, we construct some families which fail the integral Hasse principle via the Brauer–Manin obstruction with some counting results of similar nature to those in recent works of Ghosh and Sarnak; Loughran and Mitankin; and Colliot-Thélène, Wei, and Xu. We also give some counterexamples to strong approximation which can be explained by the Brauer–Manin obstruction, and study a few aspects of rational points on affine surfaces.